On written chat medium, such as IRC, many users feel that people who terminate their sentences using a full stop period come off as pedantic, or perhaps even as stating without expecting an answer, or being "closed". It may also give an appearence of seriousness, soberness, perhaps even of arrogance, depending on the scenario.
On the other hand, being a written medium, some also feel that standard writing conventions apply when chatting, including properly terminating sentences.
My impression is that chat stands in-between normal writing, which usually is unidirectional until the end of the text, and speech, where conversations are more spontanous, bidirectional. In conversation, there usually are different social conventions, and people who speak exactly like they would write can also often appear to be overly pedantic, perhaps even superficial. It is likely that in a light conversation setting, the overly pedantic speaker engages less open exchanges with others. This can even reminds us of the "uncle stating the obvious" stereotype and of listening to a speech.
This also shows the importance of emoticons, like smilies, on chat media. It is often difficult to perceive the emotions of the participants, unlike when having access to extra information like facial expressions and voice tone. Precisely, during a live chat conversation, a sentence may easily appear as cold, even if this was not the intention of the issuer. This most often occurs when one expresses disagrement. Using a full stop may make it even worse.
I don't think that a universal recipe can fit all scenarios, but I think that it is important that people participating in live chat be aware of these issues. Usually, this is enough for them to adapt as needed to ensure that they properly communicate the message as they truely intend to.
Deciding to drop the full stop in some circumstances, and adding an occasional emoticon, can often help to convey emotions felt by the participant more effectively. Using the full stop on purpose is of course also an option, to express that we feel that the conversation is over, or to express the strong intent of a refusal. Depending on the setting, in more formal or technical situations, it may also be appropriate to follow all standard rules of writing. Everything is relative.